https://github.com/maxkapur/optimalapplication.jl
Exact, approximate, and heuristic algos for the college application problem.
https://github.com/maxkapur/optimalapplication.jl
college-application combinatorial-optimization julia
Last synced: 2 months ago
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Exact, approximate, and heuristic algos for the college application problem.
- Host: GitHub
- URL: https://github.com/maxkapur/optimalapplication.jl
- Owner: maxkapur
- License: mit
- Created: 2022-02-24T23:50:49.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2025-02-23T20:32:04.000Z (3 months ago)
- Last Synced: 2025-02-23T21:18:52.199Z (3 months ago)
- Topics: college-application, combinatorial-optimization, julia
- Language: Julia
- Homepage:
- Size: 37.4 MB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# OptimalApplication.jl
[](https://maxkapur.com/OptimalApplication.jl/stable/)
[](https://maxkapur.com/OptimalApplication.jl/dev/)
[](https://github.com/JuliaTesting/Aqua.jl)
Optimal college application strategy with homogeneous and heterogeneous application costs.
Basic usage:
````julia
julia> using OptimalApplication
julia> mkt = SameCostsMarket(
# Probability of getting into each school
[0.2, 0.5, 0.1, 0.6, 0.1],
# Utility values
[1, 4, 9, 1, 8],
# Number of schools `h` to apply to. By nestedness property,
# we can obtain the solution for all `h` by setting `h = m`,
# where `m` is the number of schools in the market.
5
);
julia> x, v = applicationorder_list(mkt)
([2, 3, 5, 4, 1], [2.0, 2.7, 3.24, 3.483, 3.5154])
julia> x[1:4], v[4]
([2, 3, 5, 4], 3.483)
````
This means that when `h = 4`, the optimal portfolio is `{2, 3, 5, 4}` and its valuation is `5.408`.
The function `applicationorder_heap()` works the same way but uses a different internal data structure and may be faster for certain instances.
Example with varied costs:
````julia
julia> mkt = VariedCostsMarket(
# Probability of getting into each school
rand(50),
# Utility values
rand(40:60, 50),
# Cost of applying to each school
rand(5:10, 50),
# Budget to spend on applications
100
);
julia> x, v = optimalportfolio_dynamicprogram(mkt)
([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 38, 35, 28], 59.66127736008859)
````
For a large market like this, we may be content with an ε-approximate solution:
````julia
julia> x, v = optimalportfolio_fptas(mkt, 0.25)
([26, 46, 50], 59.623041055190996)
````
The value `ε = 0.25` means that the value is guaranteed to be no worse than `1 - 0.25` times the value of the optimal portfolio. As we can see above, the typical optimality gap is often much tighter.
The package also includes `optimalportfolio_enumerate()` and `optimalportfolio_branchbound()`, which are inefficient algorithms of primarily theoretical interest.
Finally, we can check the expected value of an arbitrary portfolio using `valuation()`:
````julia
julia> valuation([20, 16, 35], mkt)
35.33785503577366
````
## arXiv paper
If you found this package useful, please consider citing [our arXiv paper](https://arxiv.org/abs/2205.01869). Rolling updates to the paper can be found on the companion repository [CollegeApplication](https://github.com/maxkapur/CollegeApplication).